Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces

We prove an analogue of a theorem of Pollington and Velani (Sel Math (N.S.) 11:297–307, 2005), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof incorporates the framework of intrinsic approximation on such hypersurfaces first developed in the authors’ joint work with Kleinbock (Intrinsic Diophantine approximation on manifolds, 2014. arXiv:1405.7650v2) with ideas from work of Kleinbock et al. (Sel Math (N.S.) 10:479–523, 2004).